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@article{30208, author = {Smítal, Jaroslav and Štefánková, Marta and Balibrea, Francisco}, article_location = {Singapore}, article_number = {8}, doi = {http://dx.doi.org/10.1142/S021812741850102X}, keywords = {Nonautonomous systems; chaos; generic properties; topological entropy; horseshoe}, language = {eng}, issn = {0218-1274}, journal = {International Journal of Bifurcation and Chaos in Applied Sciences and Engineering}, title = {On Generic Properties of Nonautonomous Dynamical Systems}, url = {https://www.worldscientific.com/doi/abs/10.1142/S021812741850102X}, volume = {28}, year = {2018} }
TY - JOUR ID - 30208 AU - Smítal, Jaroslav - Štefánková, Marta - Balibrea, Francisco PY - 2018 TI - On Generic Properties of Nonautonomous Dynamical Systems JF - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering VL - 28 IS - 8 SP - "1850102-1"-"1850102-7" EP - "1850102-1"-"1850102-7" PB - World Scientific Publishing Co. Pte Ltd SN - 02181274 KW - Nonautonomous systems KW - chaos KW - generic properties KW - topological entropy KW - horseshoe UR - https://www.worldscientific.com/doi/abs/10.1142/S021812741850102X L2 - https://www.worldscientific.com/doi/abs/10.1142/S021812741850102X N2 - We consider nonautonomous dynamical systems consisting of sequences of continuous surjective maps of a compact metric space X . Let F-0, F-e and F-p, denote the space of systems F = (f(n))(n >= 1), which are uniformly convergent, or equicontinuous, or pointwise convergent (to a continuous map), respectively. We show that for X = I := [0, 1], the generic system in any of the spaces has infinite topological entropy, while, if X is the Cantor set, the generic system in any of the spaces has zero topological entropy. This shows, among others, that the general results of the above type for arbitrary compact space X are difficult if not impossible. ER -
SMÍTAL, Jaroslav, Marta ŠTEFÁNKOVÁ a Francisco BALIBREA. On Generic Properties of Nonautonomous Dynamical Systems. \textit{International Journal of Bifurcation and Chaos in Applied Sciences and Engineering}. Singapore: World Scientific Publishing Co. Pte Ltd, roč.~28, č.~8, s.~''1850102-1''-''1850102-7'', 7 s. ISSN~0218-1274. doi:10.1142/S021812741850102X. 2018.
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